Question

Structures of Expression Unit Test:
Use the following multiplication problem to show how multiplication polynormials is a closed system. In 2 steps.
( x2 - 1) ( -2+ 5)

Answer 1

To demonstrate how multiplying polynomials is a closed system, we will multiply the given polynomials \((x^2 - 1)\) and \((-2 + 5)\) in two steps.

### Step 1: Simplify the Second Polynomial
First, simplify the second polynomial:
\[
-2 + 5 = 3
\]
Now our expression becomes:
\[
(x^2 - 1)(3)
\]

### Step 2: Distribute (Multiply)
Now, we distribute \(3\) across the terms in the first polynomial:
\[
3(x^2 - 1) = 3x^2 - 3
\]

### Final Result
The result of the multiplication is:
\[
3x^2 - 3
\]

### Conclusion
The final expression, \(3x^2 - 3\), is still a polynomial, demonstrating that the operation of multiplying polynomials (a polynomial of degree 2 with a constant) results in another polynomial. This shows that the system is closed under multiplication.